Approximation algorithm for the weighted flow-time minimization on a single machine with a fixed non-availability interval

In this article, we consider the non-resumable case of the single machine scheduling problem with a fixed non-availability interval. We aim to minimize the weighted sum of completion times. No polynomial 2-approximation algorithm for this problem has been previously known. We propose a 2-approximation algorithm with O(n²) time complexity where n is the number of jobs. We show that this bound is tight. The obtained result outperforms all the previous polynomial approximation algorithms for this problem.